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on Econometric Time Series |
| By: | Francesco Angelini; Massimiliano Castellani; Simone Giannerini; Greta Goracci |
| Abstract: | Many macroeconomic time series are characterised by nonlinearity both in the conditional mean and in the conditional variance and, in practice, it is important to investigate separately these two aspects. Here we address the issue of testing for threshold nonlinearity in the conditional mean, in the presence of conditional heteroskedasticity. We propose a supremum Lagrange Multiplier approach to test a linear ARMA-GARCH model against the alternative of a TARMA-GARCH model. We derive the asymptotic null distribution of the test statistic and this requires novel results since the difficulties of working with nuisance parameters, absent under the null hypothesis, are amplified by the non-linear moving average, combined with GARCH-type innovations. We show that tests that do not account for heteroskedasticity fail to achieve the correct size even for large sample sizes. Moreover, we show that the TARMA specification naturally accounts for the ubiquitous presence of measurement error that affects macroeconomic data. We apply the results to analyse the time series of Italian strikes and we show that the TARMA-GARCH specification is consistent with the relevant macroeconomic theory while capturing the main features of the Italian strikes dynamics, such as asymmetric cycles and regime-switching. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.00444&r=ets |
| By: | Carriero, Andrea; Clark, Todd E.; Marcellino, Massimiliano; Mertens, Elmar |
| Abstract: | VARs are a popular tool for forecasting and structural analysis, but ill-suited to handle occasionally binding constraints, like the effective lower bound on nominal interest rates. We extend the VAR framework by modeling interest rates as censored observations of a latent shadow-rate process, and propose an efficient sampler for Bayesian estimation of such 'shadow-rate VARs.' We analyze specifications where actual and shadow rates serve as explanatory variables and find benefits of including both. In comparison to a standard VAR, shadow-rate VARs generate superior predictions for short- and long-term interest rates, and deliver some gains for macroeconomic variables in US data. Our structural analysis estimates economic responses to shocks in financial conditions, showing strong differences in the reaction of interest rates depending on whether the ELB binds or not. After an adverse shock, our shadow-rate VAR sees a stronger decline of economic activity at the ELB rather than when not. |
| Keywords: | Macroeconomic forecasting, effective lower bound, term structure, censored observations |
| JEL: | C34 C53 E17 E37 E43 E47 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdps:142023&r=ets |
| By: | Shahnaz Parsaeian (Department of Economics, University of Kansas, Lawrence, KS 66045) |
| Abstract: | This paper develops an efficient Stein-like shrinkage estimator for estimating slope parameters under structural breaks in seemingly unrelated regression models, which is then used for forecasting. The proposed method is a weighted average of two estimators: a restricted estimator that estimates the parameters under the restriction of no break in the coefficients, and an unrestricted estimator that considers break points and estimates the parameters using the observations within each regime. It is established that the asymptotic risk of the Stein-like shrinkage estimator is smaller than that of the unrestricted estimator, which is the method typically used to estimate the slope coefficients under structural breaks. Furthermore, this paper proposes an averaging minimal mean squared error estimator in which the averaging weight is derived by minimizing its asymptotic risk. The superiority of the two proposed estimators over the unrestricted estimator in terms of the mean squared forecast errors are also derived. Further, analytical comparison between the asymptotic risks of the proposed estimators is provided. Insights from the theoretical analysis are demonstrated in Monte Carlo simulations, and through an empirical example of forecasting output growth rates of G7 countries. |
| Keywords: | Forecasting; Seemingly unrelated regression; Structural breaks; Stein-like shrinkage estimator; Minimal mean squared error estimator |
| JEL: | C13 C23 C52 C53 |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202308&r=ets |